INFLUENCE OF ADDITIONAL FOOD AND BROWNIAN MOVEMENT ON THE DYNAMICS OF PEST–PREDATOR MODEL

This study addresses the critical issue of pest impact on crop yields, emphasizing the need for effective pest control strategies. Pests, defined as organisms that detrimentally affect agricultural productivity, present a significant challenge to global farming. While farmers have access to various pest control methods, this paper highlights the superior efficacy of biological control, mainly introducing natural predators into agricultural systems. This research illustrates the potential for enhancing crop productivity through sustainable pest management practices by examining an ecological model that integrates both pests and their natural predators. Throughout the study, we explored the significance of additional food and the influence of random movement on the dynamics of the model under consideration. We first examined the stability of the system near the coexistence equilibrium point. Next, we utilized Hopf bifurcation analysis to investigate the impact of extra food in the pest–predator model. Next, we examined the spatial analysis of the model by considering the Turing instability condition. This condition is responsible for the emergence of spatial Turing patterns. Our objective is to explore the impact of random movement on these patterns. We derived the amplitude equation by utilizing multiple scale analysis at the threshold value. Finally, the analytical conclusions are validated through numerical simulations. The analytical findings emphasize the intricate nature of the pest–predator system and demonstrate that when pests are not present, providing extra food can help predators thrive in the ecosystem.